Solve. 0.4y + 3 > 3.6y - 5
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Apply Inequality Theorem # 1: The direction of an inequality doesn't change if the same real number is added or subtracted to both sides
Add -3.6y to both sides, the direction doesn't change:
`0.4y-3.6+3> -5`
Add -3 to both sides, the direction doesn't change:
`0.4y-3.6y> -5-3`
Simplify each side:
`-3.2y> -8`
Apply Inequality Theorem # 2: The direction of an inequality doesn't change if both sides are multiplied or divided by the same real number.
Divide each side by 3.2, the direction doesn't change::
`-y> -8/3.2`
Apply Inequality Theorem # 3: The direction of an inequality is inverted when both sides are multiplied or divided by the same negative number.
Multiply both sides by -1, the direction changes:
`y<8/3.2`
Simplify:
`y<2.5`
Therefore this inequality is true for all values of y<2.5
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0.4y + 3 > 3.6y - 5
move like terms to the same side by subtracting 3.6y and 3
you should end up with:
.4y - 3.6y > -3 - 5
combine like terms:
-3.2y > -8
since we are solving for y we divide by -3.2
-3.2y/-3.2 > -8/-3.2
simplify:
y < 2.5
the sign changes because you are dividing.
0.4y + 3 > 3.6y - 5
To solve this , first subtract 3.6y on both sides .
By subtracting both sides by 3.6y , you should get
-3.2y + 3 > -5 now subtract 3 on both sides
By subtracting 3 on both sides , you should get
-3.2y > -5 now divide both sides by -3.2
By dividing both sides by -3.2 , you should get
y < 2.5 which is your answer
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